Penjelasan dengan langkah-langkah:

a. y = 4 ⁴√x

y = 4 . x^1/4

y' = 1/4 . 4x^-3/4

y' = x^-3/4

y' = 1/x^3/4

y' = 1/⁴√x³

b. y = 4x√x

y = 4√x³

y = 4x^3/2

y' = 3/2 . 4x^1/2

y' = 6x^1/2

y' = 6√x

c. y = -1/√x

y = -x^-1/2

y' = -(-1/2 . x^-3/2)

y' = 1/2x^-3/2

y' = 1/2√x³

y' = 1/2x√x

d. y = -5/(x²√x)

y = -5/(√x^5)

y = -5x^-5/2

y' = -5 . (-5/2)x^-7/2

y' = 25/2x^-7/2

y' = 25/2√x^7

y' = 25/2x³√x

e. y = 2 ³√x

y = 2x^1/3

y' = 2 . 1/3x^-2/3

y' = 2/3x^-2/3

y' = 2/(3 . ³√x²)

prinsip eksponen = a^m/n = ⁿ√a^m